Q. 3 - Calculus

Question

In Exercises 3–6, $\underset{x\to c}{\lim }f\left(x\right)=L$ and $\underset{x\to c}{\lim }g\left(x\right)=M$ for some real numbers L and M. What, if anything, can you say about $\underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)}$ in each case?

$L\ne 0$ and $M\ne 0$.

Step-by-Step Solution

Answer

$\underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)}=\frac{L}{M}$

Step 1. Given Information

The functions $\underset{x\to c}{\lim }f\left(x\right)=L$ and $\underset{x\to c}{\lim }g\left(x\right)=M$, where L and M are real numbers.

Step 2. Explanation.

Check $\underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)}$.

We have L and M are non-zero real numbers.

So, $\underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)}=\frac{L}{M}$